In a word, no.
Firstly, the Prodigy M isn't really upside down, it's just an awkward use of space. I'd elaborate, but it's pretty easy to see for yourself, it has (potential) intakes on the front, bottom and top and exhausts on the bottom and rear. Flipping it won't really change any of those things.
Secondly, flipping it upside down would make it incredibly top-heavy. In most cases, this wouldn't be a big deal, but the handles make Prodigy cases pretty wobbly. In fact, until you put a PSU in them as ballast, they rock very easily.
If you are set on mATX, then the Fractal Design Arc Mini or Corsair 350D are pretty popular mini towers, though it's worth pointing out the 350D isn't much smaller than a compact ATX tower. If you want a Prodigy aesthetic but a slightly less stupid layout, consider the Aerocool Dead Silence.
If you are open to format changes, it's worth considering both ITX and ATX. If you are only ever planning to use a single graphics card and want something compact, then ITX has huge potential for compact builds. If you still want a more reasonably sized board or multi graphics card support, it's worth keeping in mind that the difference in size between a mATX tower (especially one with provision for radiators like the 350D) and a compact ATX tower is pretty minimal. In most cases the least important dimension to people is the height, and that's usually all you really gain.